From an in-universe point of view, why hasn’t Katara, Tenzin, Bumi, or Kya considered communicating with their dad’s spirit through Korra, or vice versa? As of book 1, she had finally connected to her spiritual side and Aang’s spirit had manifested before her. Past Avatars have also been known to be able to posses the body of the current Avatar.
Because Aang is dead
This is a subtle distinction, but it seems that the "previous lives" scenes aren't fully-fledged conversations with fully-conscious individuals. That is, Avatar Aang can appear to Korra to convey wisdom or experience, but we never see them just "chatting," the way she does with Iroh in the spirit world. Iroh is still living a life, making friends, discovering new things, and behaving like a living, thinking person when Korra meets him. By contrast, the previous Avatars seem to only exist as advisors to the current Avatar, and seem devoid of any life (or even existence) between moments when the current Avatar needs them.
Every "past life conversation" we see onscreen follows the same structure: the current Avatar has a problem, and the past Avatar provides a story from their life to help illustrate a possible solution. If the franchise continues this may be contradicted, but so far the signs seem to indicate that the previous Avatars don't "live on" in the sense of having the ability to continue forming opinions and having experiences, but rather that they're more like a conscience or intuition, giving guidance when the Avatar needs it, based on what each incarnation learned and experienced during their life.
If this is the case, Aang's spirit wouldn't be able to "converse" with Katara through Korra at all, even if she tried. Aang is dead, and all that remains are his memories and his wisdom, which pass to his successor and are experienced as conversations.
Korra is also has a lot of issues with the spiritual side of her calling so it is difficult enough for her To contact aang, also by all accounts aang led a full happy life and his family had time to accept his passing and move on , also it would have bogged down the show with another story line it didn't need
According to the Avatar Wiki, Korra lost connection with her past lives during Harmonic Convergence. She had the ability to communicate with past avatars for only a short time.
The novel Shadow of Kyoshi speaks on this topic at length, as much of the plot centers on her trying to speak with Kuruk and her other past lives.
Communing with their past lives is one of the most difficult and complex feats an Avatar can perform... Successful methods and experiences have been known to vary between generations
More specifically, there are three options for contact, each with unique drawbacks.
There’s a number of ways Kuruk might talk to us,” he explained. “The most straightforward is if you were to simply have a vision of him. This method tends to be successful in locations with meaning for the past Avatars. This spot right here was where Kuruk would meditate and recover from his own spiritual journeys...” “The downside is that any messages you get from a vision tend to be one-way only,” Nyahitha said. “Not as useful if you have to ask him questions. Another way to have more of a conversation is if he took over your body and spoke to me in person. I would have to relay whatever you want to ask him.”Kyoshi frowned. She was distinctly uncomfortable with the idea of being possessed by someone else... “If you don’t like that, the final method, which is the most difficult and least likely to happen after one session of practice, is if you managed to meditate your way into the Spirit World. There, you could talk to him face-to-face. This is the level of communing that most people associate with the Avatar’s abilities. It’s the most efficient and clear way to draw on the wisdom of previous generations.”He paused.“But?” Kyoshi asked.“Kuruk’s spirit isn’t necessarily going to be there to greet you. And your body is rendered physically helpless while your spirit is on the other side. And sometimes you don’t remember anything you learned once you come back to the physical world.
It's clear that conferring with a previous Avatars is a complex process that can often not be done on command. As mentioned in another answer, this is especially true for an Avatar that struggles with spirituality like Korra.
- A vision
This is stated to be "one-way," so it wouldn't allow Katara to truly commune with Aang. She might not be able to even see him.
- Aang taking over Korra's body
Kyoshi is uncomfortable with this and I wouldn't be surprised if Korra was too. Much of her trauma in the show involves her sense of autonomy being violated. I doubt Katara would want this either.
- Mediate into the Spirit World
This method allows true conversation but it is stated to be especially challenging. It's not clear that that Katara could even participate either.